解方程:log2(9^(x-1)-5)-log2(3^x +2)-2=0

问题描述:

解方程:log2(9^(x-1)-5)-log2(3^x +2)-2=0

log2(9^(x-1)-5)-log2(3^x +2)-2=0
log2(9^(x-1)-5)=log2(3^x +2)+log2(4)
log2(9^(x-1)-5)=log2(3^x*4 +8)
9^(x-1)-5=3^x*4 +8
(3^x)^2/9-5=4*(3^x)+8
(3^x)^2-36*(3^x)-117=0
(3^x-39)(3^x+3)=0
又3^x>0
3^x=39
x=log3(39)